Twins Justin and Luke Lovedale, and Nicholas Gardener, screamed racist abuse as they punched and kicked their terrified victims, a court heard.
The sickening attacks were caught on CCTV inside the two stores during their night of violence, Sky News reports.
The footage was shown to Bristol magistrates' court and all three were found guilty of racially aggravated assault in both shops.
In the first attack, the two twins - who were 16 at the time - punched and kicked a member of staff in Bargain Booze after they were refused vodka and cigarettes.
They pulled shopkeeper Ashok Selvam's T-shirt over his head and then rained blows down on him.
Less than an hour later, the three thugs went to Costcutter in North Street, where they were banned.
Violence flared after one of the twins tried to snatch a bottle of wine.
As shopkeeper Parakram Zala tried to call the police, Gardener punched him in the face.